Plane waves and wave packets in elementary quantum mechanics problems

1980 ◽  
Vol 1 (4) ◽  
pp. 231-240 ◽  
Author(s):  
B Diu
Keyword(s):  
Quantum Mechanics ◽  
Wave Packets ◽  
Plane Waves

LOCAL ANALYSIS BY WAVELETS VERSUS NONLOCAL FOURIER ANALYSIS

2007 ◽  
Vol 05 (01n02) ◽  
pp. 89-95
Author(s):  
J. R. CROCA
Keyword(s):  
Quantum Mechanics ◽  
Fourier Analysis ◽  
Quantum Physics ◽  
Plane Waves ◽  
Local Analysis ◽  
Mathematical Tool ◽  
Space Harmonic ◽  
New Approach ◽  
Spatial Frequencies ◽  
Temporal And Spatial

Orthodox quantum mechanics has another implicit postulate stating that temporal and spatial frequencies of the Planck–Einstein and de Broglie formulas can only be linked with the infinite, in time and space, harmonic plane waves of Fourier analysis. From this assumption, nonlocality either in space and time follows directly. This is what is called Fourier Ontology. In order to build nonlinear causal and local quantum physics, it is necessary to reject Fourier ontology and accept that in certain cases a finite wave may have a well defined frequency. Now the mathematical tool to describe this new approach is wavelet local analysis. This more general nonlinear local and causal quantum physics, in the limit of the linear approximation, contains formally orthodox quantum mechanics as a particular case.

scholarly journals Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 96 ◽  
Author(s):  
Georgi Gary Rozenman ◽  
Shenhe Fu ◽  
Ady Arie ◽  
Lev Shemer
Keyword(s):  
Quantum Mechanics ◽  
Gravity Waves ◽  
Water Waves ◽  
Water Wave ◽  
Wave Packets ◽  
Theoretical Models ◽  
Surface Gravity ◽  
Finite Width ◽  
Self Healing ◽  
Surface Gravity Waves

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

TOPOLOGICAL EFFECTS IN QUANTUM MECHANICS AND HIGH VELOCITY ESTIMATES

2011 ◽  
Vol 20 (05) ◽  
pp. 951-961 ◽  
Author(s):  
RICARDO WEDER
Keyword(s):  
Exact Solution ◽  
Quantum Mechanics ◽  
Error Bounds ◽  
High Velocity ◽  
Wave Packets ◽  
Finite Energy ◽  
Time Dependent ◽  
Rigorous Proof ◽  
Bohm Effect ◽  
Aharonov Bohm

We consider the problem of obtaining high-velocity estimates for finite energy solutions (wave packets) to Schrödinger equations for N-body systems. We discuss a time-dependent method that allows us to obtain precise estimates with error bounds that decay as a power of the velocity. We apply this method to the electric Aharonov–Bohm effect. We give the first rigorous proof that quantum mechanics predicts the existence of this effect. Our result follows from an estimate in norm, uniform in time, that proves that the Aharonov–Bohm Ansatz is a good approximation to the exact solution to the Schrödinger equation for high velocity.

scholarly journals NEW DIRAC QUANTUM MODES IN MOVING FRAMES OF THE DE SITTER SPACE–TIME

2008 ◽  
Vol 23 (22) ◽  
pp. 3707-3720 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Complete System ◽  
Plane Waves ◽  
De Sitter Space ◽  
Space Time ◽  
Principal Result ◽  
Moving Frames ◽  
De Sitter ◽  
Schrödinger Picture

Recently a new time-evolution picture of the Dirac quantum mechanics was defined in charts with spatially flat Robertson–Walker metrics, under the name of Schrödinger picture (I. I. Cotăescu, Mod. Phys. Lett. A22, 2965 (2007)). In the present paper, new Dirac quantum modes are found in moving charts of the de Sitter space–time using the technical advantages offered by this picture. The principal result is a new set of energy eigenspinors which behave as polarized plane waves and form a complete system of orthonormalized solutions of the free Dirac equation.

From Monochromatic Plane Waves to Wave Packets

2021 ◽  
pp. 137-144
Author(s):  
Salvatore Capozziello ◽  
Wladimir-Georges Boskoff
Keyword(s):  
Wave Packets ◽  
Plane Waves

scholarly journals The Stationary Frontal Wave Packet Spontaneously Generated in Mesoscale Dipoles

2008 ◽  
Vol 38 (1) ◽  
pp. 243-256 ◽  
Author(s):  
Álvaro Viúdez
Keyword(s):  
Wave Packet ◽  
Wave Packets ◽  
Plane Waves ◽  
Three Dimensional ◽  
Vertical Shear ◽  
Vertical Column ◽  
Vortical Structures ◽  
Frontal Wave ◽  
Fluid Particles ◽  
Balanced Flow

Abstract Three-dimensional numerical simulations of rotating, statically and inertially stable, mesoscale flows show that wave packets, with vertical velocity comparable to that of the balanced flow, can be spontaneously generated and amplified in the frontal part of translating vortical structures. These frontal wave packets remain stationary relative to the vortical structure (e.g., in the baroclinic dipole, tripole, and quadrupole) and are due to inertia–gravity oscillations, near the inertial frequency, experienced by the fluid particles as they decelerate when leaving the large speed regions. The ratio between the horizontal and vertical wavenumbers depends on the ratio between the horizontal and vertical shears of the background velocity. Theoretical solutions of plane waves with varying wavenumbers in background flow confirm these results. Using the material description of the fields it is shown that, among the particles simultaneously located in the vertical column in the dipole’s center, the first ones to experience the inertia–gravity oscillations are those in the upper layer, in the region of the maximum vertical shear. The wave packet propagates afterward to the fluid particles located below.

Sign in / Sign up

Export Citation Format

Share Document